When I registered my bike two years ago here in Idaho, it took a little time to explain to the ladies at the DMV what it was, and they had to go into a side office and ask someone else some questions, but in the end they registered my bike as an off-road bike, a street-legal bike and a snowmobile. My bike's VIN is on all three registrations. I just got the renewal in the mail last week and as far as the state of Idaho is concerned, it's a Yamaha snowmobile.
It's surprising that other states would be sticky on this, since it will only increase their revenue if they just allow the bikes to be registered as sleds.
I grew up in Montana, and it doesn't surprise me that they're a little weird about it. I always felt like the people making the rules in that state were quite anti motorized recreation. I always felt like an outlaw there. "When in doubt, lock 'em out!"